$$$y^{x}$$$ の $$$x$$$ に関する積分
入力内容
$$$\int y^{x}\, dx$$$ を求めよ。
解答
Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=y$$$:
$${\color{red}{\int{y^{x} d x}}} = {\color{red}{\frac{y^{x}}{\ln{\left(y \right)}}}}$$
したがって、
$$\int{y^{x} d x} = \frac{y^{x}}{\ln{\left(y \right)}}$$
積分定数を加える:
$$\int{y^{x} d x} = \frac{y^{x}}{\ln{\left(y \right)}}+C$$
解答
$$$\int y^{x}\, dx = \frac{y^{x}}{\ln\left(y\right)} + C$$$A
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